Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-09-19
JHEP 0209 (2002) 040
Physics
High Energy Physics
High Energy Physics - Theory
10 pages, 2 figures, LaTeX, reference added
Scientific paper
10.1088/1126-6708/2002/09/040
We discuss issues relating to the topology of Euclidean de Sitter space. We show that in (2+1) dimensions, the Euclidean continuation of the`causal diamond', i.e the region of spacetime accessible to a timelike observer, is a three-hemisphere. However, when de Sitter entropy is computed in a `stretched horizon' picture, then we argue that the correct Euclidean topology is a solid torus. The solid torus shrinks and degenerates into a three-hemisphere as one goes from the `stretched horizon' to the horizon, giving the Euclidean continuation of the causal diamond. We finally comment on the generalisation of these results to higher dimensions.
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